DESIGN OF LARGE BRIDGES WITH 
SPECIAL REFERENCE TO THE 
QUEBEC BRIDGE 


; BY 
RALPH MODJESKI, D.Eng., 


_ Consulting Engineer, 
Member of the Institute. 


REPRINTED FROM THE JOURNAL OF THE FRANKLIN INSTITUTE, SEPTEMBER, 1913 





PRESS OF 


J. B. LIPPINCOTT COMPANY 
: 1913 








(REPRINTED FROM THE JOURNAL OF THE FRANKLIN INSTITUTE, 
SEPTEMBER, I9I3.) 


DESIGN OF LARGE BRIDGES WITH SPECIAL 
REFERENCE TO THE QUEBEC BRIDGE.* 


BY 
RALPH MODJESKI, D.Eng., 


Consulting Engineer, 
Member of the Institute. 


It is rather a difficult matter to draw a line between a large 
bridge and one of ordinary size. My definition of a large bridge 
would be a bridge which involves a considerable expenditure of 
money, or presents unusual difficulties of construction, or both. 
Bridges which by force of circumstances and local conditions 
span long distances may, therefore, be classed as large bridges. 
It has been my good fortune to be connected with the design 
and construction of several large bridges, and | shall deal, in the 
course of this paper, with the salient features of those struc- 
tures, while at the same time trying to deduce a few general 
\. principles which should govern the design of large bridges. I 
“shall also refer to structures designed by other engineers. It 
would, of course, be impossible in a single paper to cover the 
field in detail and in an exhaustive manner; I can only bring 
out some of the more important questions ‘which should’ be 
considered by the designer of such structures. In what follows, 








eS * Presented at the meeting of the Mechanical and Engineering Section 
held Thursday, May I, IQ13. 


497 . 


240 ne MopJESKI. SNR Were eo 


the Quebec Bridge, with its single span of 1800, feet, 100 
feet longer than the Firth of Forth Bridge,’ will be referred to 
frequently. As that bridge is now under construction, and as 
the first attempt to build it resulted in a great disaster, the structure 
will be of particular interest. 

Location.—The first question which the engineer has to deal 
with, when considering a bridge project, is the location. In the 
majority of cases this location has previously been fixed, either 
exactly or within a small range. Whenever this location is not 
fixed exactly, the engineer makes surveys of the various possible 
locations, from which surveys preliminary sketches are drawn 
and estimates prepared. One of the most important conditions 
to consider in this comparative study is the character of the 
foundations. Complete borings to determine the kind and 
quality of the material through which the foundations are to be 
built, and on which the finished work is to rest, are indispen- 
sable. In the case of a railroad bridge it is not always the location 
giving the cheapest bridge which gives the most economical re- 
sults. As an instance, let us consider the Celilo Bridge across 
the Columbia River. A bridge at the Dalles, 12 miles below 
Celilo, would have been cheaper, but the bulk of the traffic over 
this bridge being east-bound, the location at Celilo was, on the 
whole, more economical, as saving about 24 miles in the dis- 
tance to be traversed by such east-bound traffic. Another im- 
portant feature in deciding on a location is the permanency of 
the river bed. A bridge should not be located where there is 
a reasonable possibility that the stream may change its course. 
If such a location is unavoidable, the shores should be protected 
and the river regulated for some distance above the bridge. 

When the location has finally been fixed, more borings should. 
be taken, several at each pier, to establish beyond any reasonable 
doubt the character of the materials. J am laying great stress 
on this point, because it is so frequently neglected. Such neglect 
often results in serious disappointment as to the ultimate cost 
of the bridge, in differences as to settlement with the contrac- 
tors, and in delays. 

-- Length of Spans.—While sometimes the length of spans. is 








*The span of the Forth Bridge is sometimes erroneously given as 1710 
feet. This is the distance between centres of main end uprights, but the 
distance between centres of bearings at the bottom chord is 1700 feet. 


Sept., 1913.1 DeEsIGN OF LARGE BRIDGES. 241 


governed by the cost of the foundations and piers, more often 
such length of spans is fixed by requirements of navigation or 
other circumstances. The Government, in giving permission to 
build a bridge over navigable waters, generally imposes the clear 
opening of one or more spans, and passes on the design as a 
whole. It also imposes the minimum clear height above water. 
Sometimes the ruling of the Government results in an injustice 
to the railway corporations, as for instance in the case of the 
Memphis Bridge. The minimum clear height imposed for this 
bridge by the War Department was 75 feet above highest water 
known. A clear headroom of 65 feet would have been sufficient, 
and, if permitted, would only have involved the removal of use- 
less ornaments on pilot-houses of three or four boats, and a 
provision for lowering the smokestacks on a few boats, similar 
to the provision existing in the Ohio River, where the required 
clear headroom above high water is only 53 feet. ‘The addi- 
tional ten feet not only increased the cost of the bridge consid- 
erably, but resulted in heavy grades in the approach in Memphis 
and a disturbance in street grades.” 

Often draw spans or movable bridges are required over 
streams where there is no navigation, on the thecry that some 
boat might wish to come through some day. But it must be said 
that in the majority of cases the rulings of the Government 
engineers are just and necessary for the proper protection of 
navigation. Where no limitation is placed by the Government 
as to length of all spans, as in the Columbia River Bridge at Van- 
couver, for instance, in which only the lengths of the draw span 
and of the adjacent or raft span were stipulated, the spans should 
be made of economical length, provided the piers do not reduce 
the cross-section of the river sufficiently to cause an undesirable 
increase in the current velocity. This economical length may be 
determined by trials, and will be attained approximately when 
the cost of the superstructure and of the substructure are nearly 
equal. ‘This well-known principle has been applied in determin- 
ing the length of the six 265-foot spans of the Columbia River 
Bridge (Plate: I). 

The charter for the Thebes Bridge provides that it “ shall 
have at least one channel span, with a clear channel way at low 





* See Geo. S. Morison: A Report to Geo. H. Nettleton on the Memphis 
‘Bridge, 1804. . 


242 RatpH MOopDJESKI. J. ok 
| My 

water of not less than 650 feet, and all other spans over the 
waterway, at a bank-full stage, shall each have a clear channel 
way at low water of not less than 500 feet, and all such spans 
shall have a clear headroom of not less than 65 jfeet, etc.” So 
here the length of spans as well as the clear headroom is 
definitely fixed by the Government requirements. 

In the case of the Quebec Bridge, while the navigation in- 
terests fixed the clear height of the structure above high water 
at 150 feet, the length of span is entirely due to the physical 


BIG. 4. 





Original project for the Quebec Bridge in 1884-1885 by Messrs James Brownlee, A. Luders. 
Light, and T. Claxton Fidler. 


conditions of the crossing. ‘The stream at this point is narrow 
and deep, the depth in the centre of the stream being about 190 
feet. The current velocity at ebb-tide is very high—about nine 
miles per hour. Very heavy ice runs at times and tends to 
gorge. The bed rock, as shown by the borings, while accessible 
near the shore lines, dips rapidly towards the centre of the 
stream. All these conditions made it imperative to build a span 
of great length. The information as to bed rock which we now 
have would indicate that the original project could have been. 
designed with a somewhat shorter span. Yet we should remem- 
ber that this original project was undertaken by a private cor- 


Sept., 1913.] DrEsIGN OF LARGE BRIDGES. 243 


poration, and we should perhaps recognize the value to it of 
such advertisement as the building of the longest span in the 
world would obviously afford. The next longest span is that of 
the Firth of Forth Bridge, and is 1700 feet long. It is doubtful 
if a shorter span than 1700 feet would have been practicable at 
the location adopted for the Quebec Bridge. I consider it per- 
fectly legitimate to build a more expensive structure than 
economy of the work itself would call for, if the more expensive 
structure will afford sufficient advertisement and publicity to 
compensate for the additional expenditure. Cases also often 
arise where a purely economical and utilitarian structure would 
be entirely out of harmony with the surroundings. We have a 
good illustration of this policy in the magnificent stations which 
the railway companies are constantly building. 

A project to build a large bridge at Quebec, presumably in 
the same location as the present one, was seriously considered 
in 1884 and 1885. Messrs. James Brownlee, A. Luders Light, 
and T. Claxton Fidler designed a structure with a clear span of 
1442 feet? (Fig. 1). The description of that project men- 
tions rock: foundations. ‘The more complete information we 
now have, and which was obtained by a costly series of borings, 
shows that at the present location rock could not have been at- 
tained in both piers with any known method of foundation if the 
piers had been spaced only 1442 feet apart, even if the great 
depth of water could have been overcome. 

It may be remembered that after the disaster of August 29, 
1907, the Dominion Government took up the reconstruction of 
this bridge. A board of three engineers, including myself, was 
appointed to design and construct the bridge. After some study 
of the situation, the board decided that the new bridge should 
be made wider between trusses and designed to carry heavier 
loads than those originally contemplated; that, further, none of 
the old steel work could be used to advantage. It also decided 
to keep the same location. To discuss the reasons for these con- 
clusions would take up too much space in this paper. The final 
outcome is a double-track span of 1800 feet, with a width of 88 
feet between centres of trusses, designed to carry on each track 
a live load consisting of two E 60 engines * placed in any posis 





* London Engineering, vol. xxxix, 1885, p. 336. 
*Theodore Cooper’s specifications. 


244 RALPH MODJESKI. er Fhe 


tion in a train weighing 5000 pounds per foot so as to produce 
greatest strains. The old piers were not large enough for the 
new design and could not, therefore, be used. The centre line 
of the bridge running north and south the two main piers on 
each side of the stream will be designated as north pier and south 
pier respectively. At first the board contemplated building 
an entirely new pier 57 feet south of the present north pier, 
and enlarging the foundation of the south pier by sinking 
additional caissons adjacent to the old caisson. The neces- 
sary span length would then have been 1758 feet, and it was 
on that length of span that tenders were asked. It developed 
later, from the experience of sinking the north caisson, 


Pigs 2: 





Aqueduct of Gard at Nimes, France. 


that the method proposed for enlarging the south foundation 
would not be safe, even if it were practicable, and so an entirely 
new foundation and pier were decided on for the south shore. 
The new north pier could not be placed farther out in the river 
because of the sloping bed rock and great depth of water. The 
south pier could not be placed on the north, or river, side of the 
old south pier, because of the old wreckage, so it was placed 64 
feet 8 inches south of the old pier, or as close as possible to it. 
Both new piers being placed 64 feet 8 inches south of the old 
piers, measured. between centres, the new span remains 1800 
feet long. | 
The piers are all of granite backed with concrete. There. is 
an increasing tendency now to build everything of concrete. 
Certainly, concrete is a most convenient material and quite eco- — 


Sept., 1913.1 DESIGN OF LARGE BRIDGES. 245 


nomical. When it comes, however, to providing supports for a 
very important and expensive structure, cut stone masonry 
should be used in preference to concrete, except for backing. 
There are many varieties of excellent building stone on this con- 
tinent. I have used granite, some varieties of oolitic limestone, 
also sandstone, which all show excellent lasting qualities in works 
constructed many years ago, while concrete presents some un- 
certainties and requires expert care to give good results. 
Concrete may in ages prove to be as lasting as stone masonry, 
but as yet we do not know. We know that well-constructed 
stone masonry will last for centuries. A notable example of 
this is the great Aqueduct of Gard, built by the Romans in the 
Peetcentury B.c. (Fig. 2). 

Types of Superstructure-—Having fixed the span lengths of 
a bridge, the next thing to determine is the type of superstruc- 
ture to be used. The various types usually applied to long spans 
may be classified as follows: 


iy Avrciress(steel).. 
a. Vhree-hinged. 
b. ‘lwo-hinged. 
II. Simple spans. 
III. Cantilever structures. 
a. With suspended span. 
b. Without suspended span. 
IV. Suspension bridges. 


I have purposely omitted masonry and concrete arches as 
structures not coming clearly within the scope of this paper. 
Steel arches have a rational application only where Nature has 
provided natural abutments, as at Niagara Falls, for instance, 
or where natural surroundings lend themselves to ornamental 
construction. 

Crooked River Arch.—I have recently completed an arch 
bridge for the Oregon Trunk Railway in the Crooked River 
Canyon (Fig. 3). Itisatwo-hinged spandrel braced arch. Three- 
hinged arches are now seldom used for railway bridges, because 
they are less rigid than two-hinged arches. They still have a 
good application in roof trusses which are not subject to heavy 
and rapidly-moving loads. In several large arch spans the 
central connection offered considerable difficulties. The reason 


246 RALPH MOoODJESKI. LY ae 


is that the top chords at the centre of a purely two-hinged arch 
are calculated to have stresses in them, due to dead load and 
temperature, when the span is riveted up and ready to receive 
the rolling load. ‘These stresses had to be introduced by powerful 
jacks, or other means, before the final joint could be riveted up. 
To avoid this difficulty, I have proceeded as follows in the Crooked 
River arch. It was assumed that the dead load and temperature 
stresses at 60° F. in the top chord at centre are zetommsaae 
being the case, the arch acts as a three-hinged structure under 


Figs. 





Crooked River arch. ‘View showing completed bridge. 


those conditions,—namely, with all dead load in place and at 
60° F. The span was therefore erected as a three-hinged arch 
(Figs. 4 and 5), all dead load, or the equivalent, including the 
decking, was placed thereon, and at a time when the temperature 
was very nearly 60° the centre panel of the top chord was in- 
serted and riveted up. ‘The calculations were simple. The 
dead-load stresses were calculated as in.a three-hinged arch, 
the temperature and live-load stresses as in a two-hinged arch, 
and the various results combined. This made the erection very 
simple and the ultimate distribution of stresses more accurate. | 

. A two-hinged spandrel braced arch is probably the best type 


Sept., 1913.1] DESIGN OF LARGE BRIDGES. 247 
to use for railway traffic, where the natural abutments permit of 
sufficient rise, which will often be the case where the arch type 


of bridge is a logical solution. ‘This particular type of arch is 


FIG. 4. 





Crooked River arch under construction. 


more rigid and less subject to vibration than the other types of 
arch, and presents the advantage of easier erection; which can 
then be simply performed by treating each half as a cantilever 


248 RaLpH MopjJEsKI. Uy ze 


arm held back by suitable temporary anchorages until the centre 
connection is made (Fig. ie) 

An. arch bridge is a somewhat special structure and rarely 
used for very long spans, except, as | remarked before, where 
Nature has provided abutments (Figs. 4 and 6). 


FIG. 5. 





Crooked River arch. Temporary anchors and adjustments. 


Simple Spans.—Twenty-five or thirty years ago the system 
of truss most favored for long simple spans was a double inter- 
section Pratt truss with parallel chords. Nowadays the type 
most used is a single intersection Pratt truss with subdivided 


FiGeiss 





Berne, Switzerland. A very graceful highway arch bridge. 


panels and curved top chord. Fig. 7 shows the former type being 
replaced by the latter in the Bismarck Bridge (see also Fig. 12). 
The curved top chord is an element of economy. The single 
system has also a slight advantage of more definite stresses. It 
has its disadvantages, such as, for instance, the lack of untfor- 


Sept., 1913. ] DESIGN OF LARGE BRIDGES. 249 


mity in deflection, about which I will speak more in detail in con- 
nection with cantilever system. There is no doubt that a bridge 
composed of simple truss spans is a better bridge than a cantilever 
system or a suspension design, chiefly because of its rigidity. This 
rigidity results from the fact that a load placed on one span has no 
lifting action on the adjacent spans, as in a cantilever system, or 
on other portions of the same span, as in a suspension bridge. But 
long simple spans must be erected on falsework or floated into 


rere: 





Bismarck Bridge. Replacing old spans by spans of present type. 


position. ‘The first method is often inadmissible on account of the 
necessity of keeping the channel open for navigation, as in the 
Memphis and Thebes Bridges, or excessive depth of water com- 
bined with navigation requirements, as in the Quebec Bridge, or 
other local conditions. The floating of a span into position is not 
only costly but hazardous. It has been successfully performed, 
but is not always feasible or safe (Figs. 8 and g). Then, too, 
generally speaking, a cantilever bridge is more economical for 
long spans. These considerations often lead to the adoption of a 
cantilever design in preference to simple spans. A cantilever span 


RALPH MOoDJESKI. Dh Bn 


250 


5K. 


we aw 





lle, Ky. 


isvl 


tion at Loui 


into posi 


Floating span 





Floating span into position at Louisville, Ky. 


Sept., 1913.] DESIGN OF LARGE BRIDGES. 251 


can always be erected without falsework, although the adjacent or 
anchor spans must generally be erected on falsework. Sometimes 
simple spans are erected without falsework. Fig. to shows the 
340-foot simple span over the main channel and Fig. 11 the 230- 
foot span of the Columbia River at Celilo, Ore., being erected 
as a cantilever. 

The length of simple spans has been growing from year to 
year. It may be remembered that the Cincinnati Southern 
Bridge at Cincinnati, built in 1877, contains a simple span of 515 


PIG. ID. 





Columbia River Bridge at Celilo, Ore. eee 340 feet long, being erected by cantilever 
feet. In 1891 George S. Morison built the Cairo Bridge, con- 
taining a span 518 feet in length, single track. The Municipal 
Bridge in St. Louis has three simple spans of 668 feet in 
length, 110 feet high at centre, double. track and roadways. 
The Metropolis Bridge over the Ohio River, if the present design 
is carried out, will havea simple span 720 feet long, double track. 
This increase is due largely to the use of higher grade materials, 
such as nickel or chrome-nickel steel, and to the improvement in 
shop and field methods. 

And here we may say a few words about wind forces. In 


252 RALPH MOopjJEsKI. pe cea 


small spans the action of wind rarely affects the main members 
of the span, and the wind-bracing used is calculated more to . 
make the structure rigid against lateral motion under rapidly- 


HIGATE. 





Columbia River Bridge at Celilo, Ore. One of the 230-foot spans being erected by cantilever 
: method. ; 


moving loads than to take care of actual wind stresses. As the 
length of span increases, this element of wind becomes more 
and more important, until in very long spans it may become as 


Sept., 1913.1] DeEsIGN OF LARGE BRIDGES. 253 


important as the moving load. In a simple span the heaviest 
members, as well as the greatest height of truss, occur near the 
centre of the span. In other words, the resistance to wind per 
lineal foot of truss in a simple span is greatest at the centre 
of the span, and, owing to the overturning moment due to wind, 
grows in importance with the height. In a cantilever span the 
greatest height of truss and the heaviest members are near the 
piers, hence the greatest resistance to wind per lineal foot of 
truss is near the piers. This remark is sufficient to explain 


RiGee T 3. 








McKinley Bridge across the Mississippi River at St. Louis. One of three 518-foot spans. 


why wind stresses are easier to provide for in a cantilever struc- 
ture than they are in a simple span of the same length. 

I shall return later to wind forces and their importance while 
discussing provisions made for wind in the Forth and Quebec 
Bridges. 

Longest Simple Span.—No hard-end-fast rule can be laid 
down as to the length at which a simple span becomes uneco- 
nomical as compared with a cantilever span. Generally speaking, 
considering the present knowledge of materials, a simple span 
of 700 feet may be taken as the practical economical limit, be- 
yond which it is not advisable to go without a thorough inves- 
tigation and comparison with a cantilever system. Where con- 


254 RALPH MopjJESKI. Ree 


ditions require unusual methods of erection this limit may be 
much lower. For instance, in the Thebes Bridge (Plate II) it 
was necessary to erect the 671-foot channel span without false- 
work (Figs. 13 and 14). A simple span would have required 
the addition of a considerable amount of metal, both in the span 
itself and in the adjacent spans, to permit of its being erected as 
a cantilever; this excess of metal would have been useless after 
the completion of the bridge, and its cost would have made the 


BiGss ts 





Thebes Bridge. Erecting main span by cantilever method without falsework. 


bridge more expensive than the adopted cantilever design. This 
was shown to be true by careful estimates made at the time. 

General Dimensions of Simple Spans.—tIn designing long 
simple spans the following general principles should be observed. 
The width, centre to centre, of trusses should not be less than 
one-twentieth of the span, preferably one-eighteenth. In double- 
track spans the width required for clearance generally governs, 
except in very long spans. The height at centre of span, for a 
Pratt system of truss with subdivided panels, should be from 
one-seventh to one-fifth of the length. The table below shows 
the proportions of the width and height to the length of span in 
some of the curved top chord bridges built recently: 


2286 ft Jy 


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2286 5 ft Pile’ frpstle = 














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Span I-IV 
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Columbia River Bridge at_Vancouver, Washington, channel crossin, 








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Sept., 1913.1] DrEsIGN OF LARGE BRIDGES. 255 


TABLE I, 


PROPORTIONS OF SIMPLE SPANS WITH CURVED Top CHorpbs. 


Per cent. Per cent. 
ratio height ratio width 
to length to length 





Maemereminorigge, ot. Louis, Mowe... oc). eis eyes eae wines 8c oe 16.47 5.24 
Smerumeme sno, over OhioVRiver,..60) 6. ae cine sles ecse 15.41 5.60 
Pennsylvania Railroad, over Delaware, Philadelphia...... 15.70 5.82 
Gmoemormmectine Ry.-Pittsburgh 0.00. edds esse ee eee ees 14.53 5.57 
pemeereridec. ot. Lois, Mo. oe cee ee ena be tees 15.07 5.73 
Ree TICS, ot, LOUIS, AMO. ie ce ce a eee ees 14.47 5.80 
EE Ne nto fai Ks wis Chines tees hous pele ess 15.18 5.48 
feemepeeemtarek bridge, Ni- Di. ee cc eens 16.25 5.50 
Ue IGCOS SANT fo. uno oe esq sees seed sees s 17.19 = 
ee NGCT SPAN 0s ho pies os cso fuses do edee es was bee 15.03 

MEE ose Aosta vos a 'es= 6 Caron BS o BES bc ee 15.50 


The height at the ends should be only sufficient for an 
effective portal. A rigid mathematical research by Mr. Joseph 
Mayer, principal assistant engineer of the Quebec Bridge, leads 
to a theoretical proportion between the height at centre and 
length of span equal to .18, or somewhere between one-fifth and 
one-sixth, for heaviest loads and double-track spans. 

Panel Length—The best panel length is not so easy to deter- 
mine. Since the economical inclination of diagonals is very 
nearly 45°, it would result that in a Pratt truss with subdivided 
panels their length should approach one-half of the height of 
truss. This would mean that in a truss with a curved top chord 
the panels in the centre should be longer than those near the end. 
This has been done at least in one instance, namely, in the 
Municipal Bridge in St. Louis. The advantages of such an 
arrangement are a slight economy in the weight of steel and an 
improved appearance, since the diagonals have nearly the same 
inclination throughout. The equal panels, however, present, in 
my opinion, two decided advantages, which may more than 
offset the advantages of the former system, namely, that, all 
panels being equal, there is a greater duplication of parts, the 
floor beams are all alike, except at ends, the stringers are all 
alike, the length of bottom chord eyebars is the same through- 
out; and, further, that the falsework may be built in uniform 
panels; and the traveller, which is usually designed with a view 


250 RatpH Mopjeski. | . Ly; F. 1. 


to have the uprights in proper relation to the panel points, so 
that the connections may easily be made, preserves its relation to 
the various panel points as it 1s moved from panel to panel. 


FIG. 14: 


* 
“ 
> 





Thebes Bridge. One of the eight adjustment wedges by means of which the projecting arms 
were lowered and central connection made. 


For these reasons, uniform panels should be preferred in the 
majority of cases of simple spans. 
I have already stated that the greatest practical length of a 























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THE QUEBEC BRIDGE New Design 
(Qvetec, Que) 


GREAT CANTILEVER BAIDGES 


SCALE IN FEET 
0 @ oe 200 Seo 00 500F 





Sept., 1913. ] DeEsIGN OF LARGE BRIDGES. 257 


simple span is about 700 feet. With the use of certain known 
alloys of steel of greater strength than medium carbon steel this 
limit may become as much as 750 feet. Beyond this limit the 
weight of simple spans becomes so great, in comparison with can- 
tilever spans, that the latter must be considered. A mistaken idea 
sometimes prevails that the weight of steel in a span increases in 
proportion to the square of the length. This is, in a measure, 
true for short spans, say 100 to 300 feet. This ratio of increase, 
however, is not a constant, but increases with the span. A 
simple span above 1200 feet in length increases in weight ap- 
proximately as the cube of the length, and this exponent increases 
more and more rapidly until at about 2000 feet the weight of 
carbon steel required to carry the weight of such a span and 
of a moderate live load becomes infinite. For a span built of 
nickel-steel the weight becomes infinite when the length reaches 
2700 feet. Simple spans much below those limits, even if pos- 
sible, would still be very uneconomical until we get down to spans 
700 feet or under. 

Cantilever Spans.—This leads us to cantilever spans (Plates 
IllandIV). I mentioned two types of such spans: one without a 
suspended span, and the other with a suspended span. A remark- 
able example of a cantilever bridge without a suspended span, 
which may be called a semi-continuous structure, is the Blackwell’s 
Island, also called the Queensboro Bridge, in New York. There 
seems to be no advantage in omitting the suspended span; on the 
contrary, the structure differs from a true continuous bridge over 
several supports only by the introduction of a hinge at the centre 
of the main span which transmits shears but not moments. The 
vibrations and deflections of each segment are, therefore, trans- 
mitted through those hinges to all the other segments. Further- 
more, since the stresses in such a structure depend on deflections, 
there is more or less uncertainty in the calculations. I do not 
wish to be understood as objecting. to any type of structure 
seriously, because of the uncertainty of calculations. In any 
logical construction the calculations can always be made with 
sufficient accuracy for the safety of the work. It is only when 
everything else is equal that determinate stresses should be pre- 
ferred. 7 
‘~ Let ts consider the usual type of cantilever bridges, the one 
in which two cantilever arms support a suspended span. We 


258 RALPH MOopjEsKI. [Js Bead, 


may assume that in bridges requiring the construction of a canti- 
lever span the length of the main span is usually determined by 
local conditions. The general dimensions to be fixed by the de- 
signer are, therefore, the length of the suspended span, the 
length of the anchorage spans, when these are not determined 
by local conditions, the height of the trusses at various points, the 
relative distances and positions of trusses to each other. Let us 
discuss these various dimensions in connection with the new 
Quebec design (Fig. 15). The Quebec Bridge, with its longest 
span in the world, has justly attracted much attention among 
engineers and has-naturally elicited comment and criticism. It is 
acknowledged that a discussion of a scientific subject by pro- 
fessional men is often of greater value than an elaborate paper on 
this same subject by one individual. If I refer to some of the 
criticisms, let it be considered as a friendly discussion which may 
be of value to the profession. 

General Description of the New Quebec Bridge-—The new 
Quebec Bridge has been finally designed with two anchor arms 
515 feet long, a suspended span 640 feet long, and two cantilever 
arms 580 feet long. The moving loads finally adopted for the 
Quebec Bridge are: on each track two Cooper’s Class E-60 en- 
gines, followed or preceded, or followed and preceded, by a 
train load of 5000 pounds per foot per track. In addition to the 
actual dead load of the structure, a load of 500 pounds per 
lineal foot on suspended span and 800 pounds on balance of 
bridge was allowed for snow. | 

Wind Loads.—The wind loads were taken as follows: A 
wind load normal to the bridge of 30 pounds per square foot of 
the exposed surface of two trusses and one and a half times the 
elevation of the floor (fixed load), and also 30 pounds per 
square foot on travellers and falsework, etc., during erection. 

A wind load on the exposed surface of the train of 300 
pounds per lineal foot applied nine feet above base of rail 
(moving load). ; 

~* A wind load parallel with the bridge of 30 pounds per square 
foot acting ‘on one-half the area assumed for normal wind 
pressure. F . 

In the Forth Bridge the enormous wind load of 56 pounds 
per square foot was assumed. This load was imposed on the 
designers by the Board of Trade soon after the Tay Bridge 


259 


ES. 


N OF LARGE BRIDG 


ESIG 


D 


Sept., 1913.] 


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260 RALPH MOoODJESKI. [J. F. 1. 


disaster. The Tay Bridge was not designed to withstand even 
4 30-pound pressure. This assumption of a 56-pound wind in 
the Forth Bridge results in a very large addition of metal in the 
bottom chords through which the wind stresses are transmitted 
to the piers. The material in those members is distributed as 
follows: 





Dead: load Macs cieetcs oe Rene ee 2282 gross tons 
Live. foad... tai wots eeedee | come ree ees 1022 gross tons 
Wind. l6ad.3 pat tee «oot ee 2920 gross tons 

Totals sn 0a easie wt scat a sen ay ae ae eae 6224 gross tons 


The metal here provided for the wind is nearly three times 
that provided for the live load, and is about 47 per cent. of the 
total required. 

In the New Quebec Bridge design the wind pressure is 
equivalent to about 35 per cent. of the uniform live load near 
the piers and to about 20 per cent. of the live load near the ends 
of the cantilever arms. 

A pressure of 30 pounds, according to German experiments 
with electric cars, would correspond to a wind of a velocity of 
over 100 miles per hour. Other experiments made at various 
times on small surfaces show that a velocity of 85 miles would 
correspond to a pressure of about 30 pounds.® 

The following formula for wind pressures is generally used: 


P=kv 


in which P=pressure per square foot, v=velocity in miles 
per hour, and k =a coefficient. 

Eiffel’s two hundred or more experiments show this coeff- 
cient to vary from 0.0026 to 0.0032, and the average is 0.0030, 
which he recommends. ‘Trautwine makes k=0.0050, which 
seems too high. But, even using the latter, a pressure of 32 
pounds would correspond to a “hurricane” of a velocity of 80 
miles. The German experiments agree with Eiffel’s. Making 
k =0.0030, a pressure of 30 pounds would correspond to a 
velocity of 100 miles per hour, which, according to Trautwine, 
is a violent hurricane uprooting “ large trees.” 





*See Captain Bixby’s able research on wind pressure experiments in 
Report of Engineer Officers as to Maximum Span Practicable for Suspen- 
sion Bridges. 





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34-6 














MONONGAHELA BRIDGE BEAVER GRIDGE 





PLATE IV 























‘pec BRIDGE Quesec BrRipGe 
‘old Design/ . (1 New Design y, 





Sept, 1913. DESIGN OF LARGE BRIDGES. 261 


With a wind of this velocity there would be no traffic on the 
bridge—empty freight cars or even light passenger cars would 
be overturned. Velocities of over 85 miles may occur in cyclones 
and tornadoes over restricted areas. Such storms are very rare 
in Canada; but even should such an extraordinary disturbance 
happen, causing a wind pressure of as much as 60 pounds to be 
applied to the entire Quebec Bridge as now designed—the 
stresses in the truss members would be less than with the maxt- 
mum live load and a 30-pound wind—and although the stresses 
in the laterals would be increased above the specification limits, 
they would still remain within the elastic limit of the members. 

Length of Suspended Span.—The length of the suspended 
span does not depend merely upon the most economical distri- 
bution of material required for carrying the live loads and the 
dead load of the bridge after it is completed. Where there are no 
other considerations beyond the actual working stresses in the 
finished structure, the most economical length of the suspended 
span for a total span of 1800 feet would be in the neighborhood 
of 1000 feet. But to erect a simple span of such unprecedented 
length, either by floating or by cantilever method, would be 
impractical. Furthermore, the cantilever method of erecting a 
suspended span of even a moderate length always requires addi- 
tional material, both in the cantilever arms and in the suspended 
span, to take care of the erection stresses. The longer the sus- 
pended span in relation to the total main span, the greater will 
be the required addition—so that whether it be contemplated to 
erect the suspended span by cantilever method or by floating 
into position, the length of the suspended span finds itself limited 
not by mere economic considerations of the finished bridge, but 
by either the excess of material required during erection by 
cantilever method, and difficulties arising therefrom, or by the 
difficulties attending the floating of a very long and heavy span 
into position. These difficulties increase very rapidly with the 
length of the span to be floated. In the new design the sus- 
pended span is the longest which the board considered safe to 
float, and it fits the entire design very well. The erection of 
this span by floating made it possible to design it with the view 
to greatest economy. Its various members will not be subjected 
to any greater stresses during erection than they would be in a 
simple span of the same length resting on two piers. It was, 


262 RatpH MOopJESsKI. J. Fee 


therefore, possible to design it as economically as to weight as 
a well-designed simple span would be. It is more important to 
save weight in a suspended span than in an independent simple 
span, because each pound in the former requires several pounds 
in the entire structure to carry it. The importance of economy 
in the suspended span of the Quebec Bridge will be appreciated 
when it is considered that one pound uniformly distributed over 
the trusses of the suspended span needs 3 pounds of metal added 
to the bridge to carry it, making an addition of 4 pounds in all. 
This accounts for curved top chords in the span in question, as 
well as for the use of nickel-steel for the trusses thereof. 

Length of Anchor Arms.—l\t has been pointed out that the 
length of the anchor arms is uneconomical—that a shorter arm 
would have been cheaper. It must not be forgotten that a 
shorter anchor arm increases the pier reactions, as well as the 
steel in the anchorage proper. ‘he present anchor piers are 
founded on rock ledges which dip rapidly toward the river. To 
move them nearer to the river would have involved much more 
expensive foundations. 

It may be remarked here that, while an addition of dead 
load in the main span will require several times the weight of 
metal to carry it, an addition of dead load in the anchor arm 
requires no increase of metal to carry it when there is an upward 
or negative reaction on the anchor pier. This is explained by 
the fact that any load placed between the main piers or on the 
main sparis increases all moments and shears over all the spans, 
while any load placed on the anchor arm, if the reaction on the 
anchor pier is negative, decreases that reaction and consequently 
the moments in the anchor arm, but has no effect whatever on 
the main span. For this reason carbon steel will be used mostly 
in the anchor arms of the new design. ‘The carbon steel unit 
stresses adopted for the Quebec Bridge are generally five- 
sevenths of the nickel-steel stresses, the former requiring heavier 
members. This additional weight in the anchor arms is a source 
of economy when the relative prices of carbon and nickel-steel 
are considered. 

Height Over Piers.—An opinion has been expressed that the 
height over the piers of the new Quebec Bridge is not great 
enough for economy. Actual calculations show that for economy 
the height of 310 feet in the Quebec design is too great by about 


Sept., 1913.] DeEsIGN OF LARGE BRIDGES. 263 


20 feet for the ““K” system of trussing adopted; further, that 
this height would have been at least 4o feet too great.for the 
original system of the official design. The height of the Forth 
Bridge towers, while 26 feet higher than the Quebec Bridge, 
‘though the span is 100 feet shorter, is no doubt economical for 
the form of trussing adopted for it. The economical height is 
not only a function of the length of the span but also of 
the panel length next to the pier. This height should be such 
as to correspond to an inclination of the diagonals not far 
from 45°. A double intersection system with very long panels 
near the pier, such as adopted in the Forth Bridge (Fig. 16), 
would have been economical for the Quebec Bridge, except that it 


iG. 10, 





Forth Bridge. 


requires a system of secondary members or sub-posts, or very 
‘heavy longitudinal girders, or both, to carry the load from panel to 
panel. ‘Then, too, it is well to reduce in the members the stresses 
due to their own weight—which in long panels become quite im- 
portant. The 20-foot excess in height of the present Quebec 
design over what would have been the economical height is justi- 
fied by the resulting reduction in the sections of the bottom 
chords, which are of considerable size at best. 

Straight versus Curved Chords.—In long cantilever spans 
the bottom chords of the cantilever and anchor arms should be 
straight when possible. With a curved chord the joints must 
be made at the panel points. These joints are of great impor- 
tance, as has been shown in the Report of the Royal Commission 
on the Quebec Bridge Disaster. They should be fully spliced 


264 RALPH MOopDJESKI. . LJe Bed. 


to take care of secondary stresses due to deflections of the span 
during erection and under the action of live load. It is advisable, 
therefore, to place them outside of the point of connection with 
the diagonals and keep them clear of gusset plates. The same 
objection does not exist.in top chords of simple spans, which are 
of moderate sizes, even in the longest spans known. The economy 
in simple spans resulting from such curved chords is worth while 
and quite important, while if any economy were to result from 
curving the bottom chord of the cantilever and anchor spans, 
such economy would certainly be of little importance in compari- 
son with the resulting disadvantages. The vertical deflections 
from live loads are not as great in a straight chord design as in 
a curved chord design. Another consideration in favor of the 
straight chords is that the most important, in fact the bulk, of 
the wind forces travel to the pier through the bottom chords of 


the cantilever and anchor arms and the wind-bracing, or lateral~ ~ 


system situated in their plane. The straight bottom chords 
carry these stresses direct to the piers without transmitting any 
appreciable components to the web system of the trusses. Not 
so with curved bottom chords. At each joint where the chord’s 
direction is changed a component stress is transmitted to the 
web. This means that while a pair of straight chords with its 
lateral system deflects under the action of the wind in the plane 
of the chords only, a pair of curved chords, by transmitting shear 
to the web members, causes the trusses to deflect, the windward 
truss downward, tending to flatten the curve, and the leeward 
truss upward, tending to make the curve more pronounced. 
The rigidity of the straight chord design against lateral deflec- 
tions and oscillations is therefore greater than that of the curved 
chord design. 

One of the reasons why curved bottom chords were used in 
the cantilever arms of the original Quebec Bridge design was the 
fact that it was the aim of that design to provide full headroom 
of 150 feet on a width of tooo feet. The bottom chords of the 
anchor arms were then made curved also for the sake of sym- 
metry. This width on which the full headroom will be obtained 
has been reduced in the new design to about 760 feet, which 
-certainly is more than ample to accominodate navigation. Only 
the highest vessels will be limited to this width of 760 feet, and 
‘that only at high water. ‘ 3 


Sept., 1913.] DesiGN OF LARGE BRIDGES. 265 


The top chord of the Quebec Bridge cantilever and anchor 
arms is straight. The Forth Bridge cantilever arms have straight 
top chords also. While there was good reason for making the 
Forth Bridge top chord straight, there was no serious reason, 
beyond a slight increase in, vertical rigidity, for making it 
straight at Quebec. The two trusses on the Forth Bridge are 
in planes inclined toward each other at the top. The two top 
chords are parallel. Had they been made curved they could not 
have been parallel, since they must necessarily be situated in the 
inclined planes of the trusses. The appearance of tension chords 
having a greater distance apart at the centre of the arm than at 
either end would have been very bad. But there is no such 
reason at Quebec. The trusses are in vertical planes and the top 
chords could have been curved without serious inconvenience, 
but also without any advantage. ‘The board considered that, 
- -aside from the additional vertical stiffness, a straight chord will 
present an appearance of strength which a curved chord would 
not do. | 
Relative Position of Trusses—With regard to the distance 
- between trusses and their position relative to each other, the 

trusses of the new Quebec Bridge will be in two vertical and 
parallel planes. The distance, centre to centre, of trusses will 
be 88 feet. One of the first preliminary sketches made after the 
board was created contemplated placing the trusses in planes in- 
clined in the same manner as in the Forth Bridge, namely, with 
the tower posts converging toward the top and the bottom 
chords of both the anchor and the cantilever arms converging 
toward their respective ends. Another sketch contemplated 
trusses in vertical planes, but converging for the anchor and 
cantilever arms toward their respective ends. Both these plans 
would be economical in the amount of metal required in the 
finished bridge; but erection of a structure of this magnitude is 
extremely difficult, and some sacrifice of economy is necessary 
to make the field work as safe and easy as possible. It was 
during the erection that the old Quebec Bridge collapsed. ‘The 
board consulted several of the best authorities on erection of 
large structures, and, while their opinion differed somewhat, it 
was decided, after much deliberation, to make the trusses par- 
allel throughout. In doing so we had in mind not only the 
erection which was the principal consideration, but the greater 


266 RALPH MOopjEsKI. : [J.B dak 


simplicity of details at such important points as the pier posts 
and the points of suspension of the suspended span. ‘The con- 
nections at these points become quite complicated when the 
anchor arm, cantilever arm, and suspended span trusses are not 
all in the same plane. It would have been possible to design the 
bridge with trusses in two planes inclined toward each other, 
parallel to the axis of the bridge and passing through the end 
supports of each truss. In this manner all connections of truss 
members would have been nearly as simple as in the adopted 
design. Such a design was also suggested and considered. But 
it was soon decided that the erection of heavy members in an 
inclined plane of the truss would be too hazardous, and this plan 
was abandoned. A question may fairly be asked: Since the 
Forth Bridge, with its curved bottom chords, inclined and flaring 
trusses, has been so successfully constructed, why was it not 
possible to follow a similar design in the Quebec Bridge? The 
difference is all in the labor conditions prevailing on the two 
continents at the respective times of building these bridges. At 
the Forth Bridge 3200 to 4100 men were employed when the 
work was proceeding full swing; their number attained 4600 for 
a short period. At Quebec such a large force could not be mus- 
tered. The contractors contemplate now using approximately 
400 men in the field and not over 1000 including men in the 
shops. In the Forth Bridge the material was all manufactured 
at the bridge site. By using a large force of men it was possible 
to build up the various members of single plates or shapes so 
that no heavy pieces were handled. The admirable design, con- 
sisting principally of tubes, of which there are nearly six miles 
in the bridge, was built up in a similar manner as boilers are 
made—piece by piece. ‘The various connections were laid out 
in the field, plates bent to suit, drilled and riveted on. This 
method of procedure would be impossible in Quebec. Not only 
are the men not available, but while on the Firth of Forth the 
climate is such that work may go on at all seasons of the year, 
in Quebec work aloft is impossible during more than seven 
months in the year. Here, then, the bulk of the work must be 
done by machinery to save manual labor, and must be done in 
the shops to permit a continuous progress. The work in the 
field must be reduced to the minimum or to the assembling of 
large pieces—as large as it is practicable to handle. The Amer- 


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OUTLINE LUAGKYHI9 Of FICCLPTLD DESIGN AND \SIK COMPETING DELHGNS FOR THE 
NEW GULBLE OBRIDGL OYER THE 817 LAWRENCE KAIVER, NEAR GULBEC, CANADA. 





Sept., 1913.] DrEsIGN OF LARGE BRIDGEs. 267 


ican type of pin-connected construction lends itself best to these 
conditions, but with that type the details will be much simpler 
and the erection much easier with trusses situated in two vertical 
and parallel planes. 

System of Irussing.—The system of trussing was from the 
beginning the object of discussion and diversity of opinion 
among the members of the board; so much so, that before a 
definite agreement was reached it was decided to work up a plan 
which, though not satisfactory to all the members of the board, 
would, when detailed, give the first accurate estimate of weights, 
which would be also sufficiently accurate to serve as a start in 
designing any other plan of the same general dimensions. The 
plan thus detailed, though not approved, will be referred to as 
the official design. A discussion of the proceedings among the 
members of the board and the government officials, which led to 
the ultimate result, would be out of place here. Let it suffice 
that, in addition to asking for tenders on the official design, the 
bidders were requested to submit their own designs in accord- 
ance with specifications furnished by the board. The time 
allotted for preparing such designs was shorter than the time 
it took the board to prepare the official design; but it should be 
remembered that the official design furnished to the bidders 1n- 
formation which it took months of study to prepare. Not the 
least important information thus furnished was the estimate of 
- weights computed from the details of the official design. 

Selection of Design.—Several designs were submitted with 
the tenders (Plate V ) ; the design submitted by the St. Lawrence 
Bridge Company, with what may be called a “K” system of 
trussing in the cantilever arms and anchor arms, was finally 
recommended by the majority of the board and later endorsed 
by an enlarged board appointed by the Minister of Railways and 
Canals for the special purpose of selecting the best tender. The 
- main reasons for recommending the design in question are given 
in the enlarged board’s report as follows: 


(a) The type of design offers greater safety to life and 
property during erection, as well as economy and 
rapidity in construction. 





* House of Commons Debates (Canada), Tuesday, April 19, 1912, vol. 
xlvi,.No. 65, p. 5522 and following. 


268 RatpH MopjJeskI. ier 


(b) The design contains the minimum number of 
secondary members and requires few, if any, tem- - 
porary members during erection. 

(c) The system of triangulation, by dividing the web 
stresses, reduces the members to more practical 
sections and simplifies the details of connections. 

(d) The design economizes material, as shown by the 
calculated weights of the two designs. 3 

(e) The general appearance of the structure is, in 
our opinion, improved. | 


Fig. 07, 



































; 10 
Quebec Bridge, Phcenix Bridge Company design. Deformation diagram. Live load reversed. 
Scale of deformation is 120 times greater than scale of truss. 


There are two advantages of this “K” design which are 
not clearly brought out in the above reasons, and on which I 
wish to lay considerable. stress, namely, uniform deflections and 
regularity of erection operations from panel.to panel. The 
uniform deflections can best be seen by comparing the Williott’s 
diagrams. Figs. 17 to 22 show the deflections of the anchor 
arm under dead load and under dead and full live load in the 
old, the official, and the final designs. The deformations are, of 
course, on an exaggerated scale. A comparison of these diagrams 
will show that secondary members, or those which receive their 


eo, 


Sept., 1913.1 DESIGN OF LARGE BRIDGES. 269 


maximum stress from partial live load only, such as the vertical 
suspenders carrying one panel of floor (Figs. 17 and 18), or 
members which carry dead load only, such as vertical sub-posts 
supporting the top chord, or members which normally have no 
stress in them, such as struts which serve to reduce the unsup- 
ported length of main compression members, are the source of 
local bending in the main members to which they connect. This is 
because the variation in length of the secondary members as 
the loads are applied is independent of the variation in length 
of the main members. For instance, a secondary member car- 


Fic. 18. 























Quebec Bridge, official design. Deformation diagram. Live load reversed. 
Scale of deformation is 120 times greater than scale of truss. 


rying dead load only receives its full deformation in length 
_ when the span is finished, but its length remains constant under 
any condition of live load, while the adjoining main members 
compress or elongate with each application of live load. In 
the safne manner a suspender carrying one panel of the floor, 
for instance, will receive its maximum elongation under con- 
centrated live load in ‘this panel whether the remainder of the 
bridge is loaded or not, while the adjoining main members will 
receive their maximum deformation under quite different con- 
ditions of loading. The bridges are generally designed in such 
a manner that the secondary stresses are either entirely elimi- 
nated or largely reduced when the main members are subject to 


270 RALPH MODJESKI. iJ. Bee 


greatest direct stresses. This is done by determining the lengths 
of the various members, both main and secondary, in such a way 
that the truss, under the maximum load, will assume as nearly 
as possible the geometrical shape. This requires, however, an 
initial displacement of the main members, which during erection 
may be very objectionable. 

The diagrams referred to show the situation as reversed, 
namely, as if the loads were applied to a truss having the true 
geometrical form. In order to obtain the true geometrical form, 


Fic. 19. 





























14 


Quebec Bridge, St. Lawrence Bridge Company design. Deformation diagram. Live load 
reversed. 


Scale of deformation is 120 times greater than scale of truss. 


after the loads are applied, we. should begin with a truss de- 
formed under condition of no load. 

The comparatively large distortions of the truss in the old 
design (Figs. 19 and 20) are due not only to greater unit stresses 
used but also to the curved bottom chord and the large number of 
secondary members. I have explained the reason why curved 
bottom chords were used in that design. Of the three designs 
shown in the diagrams, the new design has the least number of 
secondary members. It should be remarked that the same ad- 
vantage could have been obtained with a double intersection 


Sept., 1913.1] DESIGN OF LARGE BRIDGES. 275 


Warren truss by arranging the panel lengths in such a manner 
as to eliminate the intermediate vertical secondary members 
supporting the chords. (See Memphis and Forth Bridge dia- 
grams, Plate III.) It would be interesting to know the extent 
_of secondary bending stresses produced in the tubular bottom 
chords of the Forth Bridge by those vertical members, but un- 
fortunately the necessary data for their calculation are not 
available. 

The regularity of erection operations consists in the fact 


BiG: 20, 



































10 


Quebec Bridge, Phoenix Bridge Company oS Deformation diagram. Dead_,-+ live load 
reversed. 


Scale of deformation is 60 times greater than scale of truss. 


_ that, starting from the pier, the position of members. in each 
panel in the “ K ”’ design is just like the preceding one, and that 
coupling up of members in each successive panel, as the traveller 
moves forward, requires the same succession of motions as in 
the preceding one, except that pieces become lighter as the erec- 
tion proceeds. Experience shows that the oftener an erection 
crew goes through a series of the same motions, as, for in- 
stance, in erecting a succession of simple spans all alike, the 
more rapid their progress becomes. 

Some of the more important features of the Quebec design 


272 | RaLtpH Mopjeskl. . [JicEeek 


will be of interest. The lateral wind-bracing has been omitted 
between the top chords of the cantilever and anchor arms. All 
wind forces are taken directly to the pier through substantial 
bracing between the bottom chords. This arrangement not 
only makes the distribution of wind stresses perfectly definite 
but permits the spreading of tracks to 32 feet 6 inches, centre 
to centre, instead of the usual 13 or 14 feet, which results in a 
saving in the floor system, and consequently in the entire struc- 
ture. With the tracks spread, a load on one track only produces 
a torsion in the cantilevers, and the presence of wind-bracing 


Piceet 





























12 


14 
Quebec Bridge, official design. Deformation diagram. Dead + live load reversed. 
Scale of deformation is 60 times greater than scale of truss. 


between the top chords would produce undesirable and excessive 
stresses which would have to be taken care of by a large addi- 
tion of metal to the lateral and sway systems and to the trusses. 

The floor system is of carbon steel throughout. It is, there- 
fore, stiffer than if made of nickel-steel. The long floor beams 
deflect less and the secondary stresses produced by their deflec- 
tion are thus reduced. Even then some of the connections of 
floor beams to posts had to be made by means of pins. The top 
chords of the cantilever arm and of the anchor arm as now de- 
signed are of carbon steel eyebars. The originally-submitted 
design contemplated nickel-steel plates riveted throughout for 
the cantilevers, and carbon steel plates for the anchor arms. By 


Sept., 1913.1 DeEsIGN OF LARGE BRIDGES. 272 


substituting eyebars a better design is obtained and much easier 
erection assured, and, although nickel-steel is replaced by carbon 
steel in the cantilever arm, the substitution results in a saving 
when both the cantilever and anchor arms are considered. Car- 
bon steel will be used in the entire anchor arm, in the top chord 
and pier members of the cantilever span in the top lateral system 
of the suspended span, in all the floor system and all sway 
bracing. Nickel-steel will be used in the trusses and bottom 
laterals of the suspended span, in the trusses except top chords 
and pier members, and in the lateral system of the cantilever 


PIGwe22- 
































/4, 


Quebec Bridge, St. Lawrence Bridge Company design. Deformation diagram. Dead + live 
load reversed. 


Scale of deformation is 60 times greater than scale of truss. 


arms. The anchor bars which hold down the ends of the anchor 
arms have been made very long to reduce bending stresses from 
expansion. , 

The suspender eyebars which support the suspended span are 
subject to oscillation in the plane of the trusses, due to expan- 
sion. A total expansion of 16 inches must be taken care of at 
these two points of suspension—besides the extension of the 
bottom chords under the live load. Manganese bronze bushings 
will be provided in these eyebars to permit of easy turning on 


274 RALPH MOoDJESKI. iy cate 


the pins. But, even should these fail to turn, there is sufficient 
metal in these eyebars to prevent overstress from bending. 

Friction brakes will be installed to prevent excessive longi- 
tudinal oscillations of the suspended span under tractive forces 
of trains. 

All latticing of compression members is designed in pro- 
portion to the sectional material of each member. The latticing 
is made strong enough to transmit in transverse shear 2 per 
cent. of the direct stress of the member. 

Determination of Dead Load.—After the designer has deter- 
mined the principal dimensions and has designed the skeleton 
outline of the bridge, the next necessary step is to calculate the 
stress sheets and proportion the various members. Assump- 
tions must first be made on the dead load of the various portions 
of the span. In simple spans and in suspension bridges a first 
assumption of a uniform load per foot is generally sufficient ex- 
cept in very long spans, in which the concentrated loads should 
be calculated after the details are designed, and the sections 
should be checked and modified if necessary. In cantilever 
structures the distribution of the dead load is a far from 
uniform (Fig. 23). 

The Forth Bridge weighs 2 tons per et at ‘tie centre of 
‘each span and 13% tons per foot near the towers. ~The new 
Quebec Bridge weighs 8.7 tons per foot near the centre and 38 
tons per foot near the piers. The original Quebec Bridge was 
underestimated—the calculated dead load stresses were too 
small; it was to guard against a similar error that the official 
design of the new bridge was worked out in detail before even 
the system of trussing was quite agreed upon. 

In calculating the weight of a span from the known weight 
of a shorter span it is customary to assume that the total weight 
of steel in trusses and bracing increases as the square of the 
span. This rule of thumb is sufficiently correct for small spans, 
not to exceed 200 or 300 feet in length, but is obviously wrong 
for very long spans. If it were true for all spans, then a span 
10,000 feet in length could be built by providing 100 times more 
metal than a span of 1000 feet would require. We know that 
a span of such length is impossible with materials now known 
and that it would fail under its own load. As a matter of fact, 
in a cantilever system of the size of the Quebec Bridge the 


2 


Sept., 1913. DEsIGN OF LARGE BRIDGES. 275 


weight of the steel increases more rapidly than the cube of the 
length. This power or exponent increases still further for 
longer spans until it becomes infinite for a span which is just 
long enough to carry its own weight only at the allowable unit 
stresses without being able to carry any live load. 


BiG. 23, 


— DIAGRAMS or WEIGHTS —— 
PER FOOT 2 BRIDGE 


MMM 
/ fa 


— WOO - xX 


EW QUEBEC 


ppp TEN 


if i Sy 


= SCALE— 
IN THOUSANDS OF LBS. 









































M4 
aN 





Wy UDSIKK JAAN 
SAX 















= ie THE 
IL K MY YE oe CXX® 


BS ATI is ATER XOXO XD RAIN IN 1 


The principal dimensions being fixed and the preliminary 
stress sheets calculated, the details of the structure must be 
worked out. Needless to say that all these determinations which 
I have mentioned as taking place in succession are correlated to 
each other, and frequent retracing of one’s steps is necessary 


276 RaLtepH MopjeEskI. Bei ey 


before the detail plans are matured. The general order of pro- 
cedure, however, is always about as described. 

Bottom Chords.—The bottom chords of the anchor and canti- 
lever arms and their details were the subject of a great deal of 
study and of many tests. Little is known about bridge com- 
pression members when compared to tension eyebars. The 
Quebec compression chords are members of unusual size. It is 
only in work of great magnitude that the engineer has an oppor- 
tunity to make tests on a large scale; the expense of such tests 
is trifling in comparison with the importance to the structure 
of the results obtained. It is not sufficient to know that in 
some bridges a compression member is still standing and is sub- 
jected to a certain stress. What we should know is how much 
greater stress it would take to destroy that member. Such a 
member may be in the stage of danger from the last straw. 
The board made a number of tests on models of chords and 
posts, both for the official design and for the final one. The 
tests gave generally better results for model members repre- 
senting the latter. ‘The board feels, therefore, that a good design 
for these heavy members has been obtained (Plate VI). 

There never was any serious doubt among the members of 
the board as to the advisability of making the bottom chords of 
the anchor and cantilever arms riveted throughout without pin 
joints, except at the main pier bearings, to avoid excessive secon- 
dary stresses. This was done and will result in a stiffer bridge. 

Top Chords.—The original design as submitted by the St. 
Lawrence Bridge Company contemplated top chords built of 
plates entirely. While this was approved at the time, later studies 
proved that by building the top chords of carbon steel eyebars 
there will be a slight saving of weight and cost, and the change 
was authorized. A tension member built of eyebars is the most re- 
liable type by reason of the large number of full-size eyebar 
tests which have been and are constantly being made. It is the 
logical form of construction for transmission of tensile stresses. 
Their use reduces the secondary stresses. In a chord built up 
of wide plates with riveted joints, making it continuous, the 
secondary stresses resulting from bending due to the deflection 
of the span would be considerable, but owing to the uniform 
deflection of the “ K ” design they could easily be taken care of. 

One of the guiding principles of the designers of the new 






PLATE VI. 





Doville Lacing 8 x/2 










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Sections oF LARGE 
COMPRESSION MEMBERS 









Scace in Feet 
ee ee 





PLATE VI. 


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THEBES BRIDGE Lower Chord- Certro/ Spar 
’ ee a Lower Chord Lo3-Lo# Cartilever Artz 
BLACKWELL'S ISLAND GRIDGE oe 


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BEAVER BRIDGE. 
Lower Chord Lele Archor Wim 



























































































































































































































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Scace in Feet 





Sept., 1913.] DeEsIGN OF LARGE BRIDGES. or 


Quebec Bridge was the elimination of untried features and ex- 
periments. In a span of this length some new features must 
necessarily be introduced, but they are limited to those only 
which grow out of the unprecedented length of span. 

Suspension Bridges.—With the length of the Quebec span 
of 1800 feet and with the materials now at the disposal of the 
engineer, the practical limit of cantilever construction has very 
nearly been reached. In fact, if economy alone is to be consid- 
ered, a cable suspension bridge would have been cheaper for a 
span of 1800 feet. ‘The cantilever structure presents a greater 
rigidity under moving load, and this greater rigidity was the 
determining factor in the decision of the board to adhere to the 
cantilever type. Tentative plans of the suspension type with 
wire cables were, however, partly worked out by the board in 
the way of study. 

The comparative rigidity of the cantilever system on one 
hand and the suspension type on the other may be gauged by the 
deflections at the centre of the span under full load. 


emer cnal, 10tal live load... 20... 00... cc ce eee ee ce eee ee 1134 inches 
A. cable suspension bridge, trial design—live load only, over.... 2 feet 
A cable suspension bridge—with 120° variation in temperature 

and full live load—between highest and lowest position 

RE SEU 9) Ae Se 7 =teet 


There are two reasons for the large deflections in suspension 
bridges: First, the deflection due to variations of temperature in 
the cables of a suspension span, which in a cantilever span is 
inappreciable; and, second, the fact that higher unit stresses are 
permissible in the wires of the cable than in the members of the 
cantilever span. The working unit stress in the wires is gen- 
erally taken at from 55,000 to 60,000 pounds, while less than 
one-third of this is permissible in rolled carbon steel. When 
a moving load travels on a suspension bridge it subjects it to 
partial deflections which may be compared to a wave motion. 
This motion is greatly obviated by the use of deep stiffening 
trusses. The deeper those trusses are, the smaller will be the 
partial deflections. It is, therefore, an advantage to make these 
stiffening trusses as deep as practical considerations will per- 
mit. But, on the other hand, the deeper the truss the more 
equalizing will it perform and, therefore, the heavier will it 


278 RaLpH MopjEskI. [Ji Peee 


have to be. Each particular case must be studied in this respect, 
taking into consideration the relative importance of the live load 
which produces these local deflections, to the dead load. A sus- 
pension bridge generally consists of one main span and two side 
spans. ‘There are two distinct types of side spans—one where 
these side spans are suspended from the cables, as in the Man- 
hattan Bridge in New York (Fig. 24), and one where they are 
supported independently of the cables, as in the Williamsburg 


Fico on 





Manhattan Bridge, New York. Showing type of suspension bridge with side spans supported 
from main cables. 


Bridge in that city (Fig. 25). There are also two types of 
stiffening trusses for the main span—a continuous truss, as in the 
Manhattan Bridge, and a truss hinged at one or more points, as in 
the Brooklyn Bridge. For a bridge for highway and street car 
traffic, even though interurban trains are to use it, the most suit- 
able type is the one with comparatively shallow stiffening girders 
continuous over the main span, with side spans suspended from 
the cables: this because of the absence of concentrated moving 
loads which would be heavy enough to cause appreciable local 
deflections. On the other hand, a bridge for railroad use, single- 
or double-track, should preferably be built with deep stiffening 
trusses over the centre span, hinged at centre or continuous, with 


Sept., 1913.] DrsiGN OF LARGE BRIDGES. 279 


side spans supported independently of the cables. It is perfectly 
practicable to build an efficient and economical suspension bridge 
for railway use if these principles are adhered to. 

The main parts of a suspension bridge are the cables. These 
are sometimes replaced by eyebar chains. The longest eyebar 
suspension bridge is in Budapest and has a span of 9&1 feet. 
The longest cable span is 1600 feet, and the one built by Roebling 
Brothers is still giving excellent service. There is no doubt, 
therefore, that the wire cable has been successful for long spans. 


FIG. 25. 





Williamsburg Bridge, New York. Showing type of suspension bridge with side span supported 
independently of main cables. 


It is doubtful if an eyebar chain suspension bridge of 1800- 
foot span would prove economical as compared with the canti- 
lever type unless some special steel with which we have had 
little experience be used. The impact from moving load in 
the chain would be within 10 per cent. of the impact produced 
in the top chords of the cantilever arms, so that much higher 
unit stresses in eyebar chain links than those used in eyebar top 
chords of the cantilevers would not be justified. The allowable 
working stress in cables is not less than 55,000 pounds per 
square inch, while it is not over 30,000 pounds in nickel-steel 
-eyebars, or a little more than one-half. . ; 

From what was said throughout this paper it is obvious that 


280 RALPH MOoDJESKI. ay Se 


the longer the span the greater the need of materials of high 
resistance. For plate girders and short spans ordinary medium 
steel does very well and is used exclusively; for longer spans, 
beginning with 400 feet, alloy steel, such as nickel-steel, nickel 
chrome, vanadium, etc., may be used to advantage, this advan- 
tage increasing with the length of span. ‘The practical limit of 
cantilever system for known materials is reached at about 2000 
feet for a railroad bridge. For longer spans, suspension bridges 
should be used, and are made possible by the high resistance of 
wire cables. The practical span limit of a wire cable suspension 
bridge has been calculated at 4335 feet, assuming a working 
stress in the cables of 60,000 pounds per square inch.’ 

The breaking load of the cables was assumed at 180,000 
pounds per square inch. If an alloy wire be used of a still 
higher resistance the practicable limit will exceed the one given 
above. The limit of length of a cable alone without any load 
except its own, stressed at 60,000 pounds per square inch, is 
15,160 feet.? ‘This assumes the versed sine of the cable to be %. 

An eyebar chain of alloy steel, such as now in use, should 
not be stressed beyond 30,000 pounds per square inch. Assum- 
ing this stress and a versed sine of 1%, the limit of length of 
such a chain will be 7o10 feet.. Hence, the limit of span length 
of an eyebar chain suspension bridge to carry live loads would 
be considerably below that of a cable suspension bridge. 

The suspension design lends itself better to graceful treatment 
than a cantilever bridge, and may often be preferred for orna- 
mental highway bridges even where a cantilever were to make 
a cheaper bridge. 

Considering the purely utilitarian structures, such as the 
majority of railroad bridges, the present knowledge of metals 
and its alloys, and the present loadings, we may sum up the 
various types of large bridges as follows: 


Foraspans pate) 750 meet. ae ee Simple spans. 
For spans from 650 feet to 2000 feet...Cantilever spans with suspended span. 
For spans from 1500 feet to 4000 feet..Cable suspension spans. 


Arch spans have their place only where natural conditions 
are favorable, or for ornamental bridges. 





“Report of Board of Engineer Officers (U. S. Army) as to Maximum 
Span Practicable for Suspension Bridges, 1894. 


Sept., 1913.] DESIGN OF LARGE BRIDGES. 281 


Chain suspension bridges may be used for ornamental high- 
way or city bridges, but for railroad service and for spans below 
1500 feet the cantilever is to be preferred as giving a stiffer and 
generally a cheaper structure. 

It will be noticed that the above limits overlap. Local con- 
ditions in each particular case will be considered in deciding 
whether a span between 650 feet and 750 feet should be simple 
or cantilever, or whether a span between 1500 and 2000 should 
be a cantilever or a suspension span. 

Secondary Stresses—I shall not dwell long on this latest 
addition to bridge calculations. That secondary stresses exist 
is a fact. They may be from three sources: 

First—Weight of member. 

Second.— Vemperature. 

Third.—Bending from loads. 

In the new Quebec design all secondary stresses were cal- 
culated and taken care of, but as a result of tests made by the 
Quebec Board, the stresses in tension members due to their own 
weight will be neglected. It is quite possible that if similar tests 
could be made for other secondary stresses it would be found 
that the metal adjusts itself to a large extent in such a manner 
as to reduce the importance of those secondary stresses and their 
influence on the elastic limit of the member. Personally, I feel 
there is a tendency at present to overrate the importance of sec- 
ondary stresses. They should, of course, be considered in de- 
signing a structure; it should be the aim of the designer to reduce 
these secondary stresses to the minimum, but excessive refine- 
ment should be avoided, and unit stresses for direct loads should 
be made low enough to include these secondary stresses where 
they may exist. 

Materials—The proper selection of materials for a struc- 
ture is an important part of the design. The ordinary com- 
mercial steel will do for rough plate girder work, but for large 
bridges a metal of higher quality should be used. The metal or 
alloy should have a high elastic limit, a high ultimate stress, and 
possess sufficient ductility, which is characterized by the elonga- 
tion and the reduction of the cross-section of specimens tested, to 
allow its being worked in the shops without fear of injury. 
Here, perhaps, climatic conditions should be mentioned. Intense 
cold makes steel brittle. This is shown by the greatly-increased 


282 a RaLtpH MopjEskI. (J-FAL 


number of rail fractures during severe winters. The use of 
high carbon steel should therefore be avoided in northern 
climates. The behavior of the various alloys in freezing weather 
needs yet to be studied. ; 

In all that precedes I have endeavored to avoid speaking of 
matters which are usually given in text-books. I have also 
avoided mathematical deductions, leaving them to better mathe- 
maticians, and I have attempted to deal with this vast subject 
from a practical standpoint only. When the final report of the 
Quebec Board is published it will give in detail what I have 
merely been able to outline. Numerous most interesting tests 
and mathematical analyses have been made and will be pub- — 
lished in the course of events. It will then, perhaps, be realized, 
even by the members of the engineering profession who had no 
opportunity to fully design a very long span, that, while it is 
very easy to draw a diagram and a few of the principal details, 
it takes months of study, of retracing one’s steps, of tests and 
calculations to make a complete design and to learn that the 
preliminary diagrams and sketch details must often be changed 
entirely to make a practicable and an efficient structure. 


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